Wormholes supported by phantom energy from Shan–Chen cosmological fluids

Abstract

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan–Chen background fluid are obtained. We have considered the important case of the model parameter ψ ≈ 1, which corresponds to the “saturation effect”, and this regime corresponds to an effective form of “asymptotic freedom” for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversablities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide −1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius.